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Complete the identity (sin x +cos x) ^2

Please please help

Complete the identity (sin x +cos x) ^2 Please please help-example-1
User Roy Shoa
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Explanation:

Using perfect square trinomial rules,


(a + b) {}^(2) = {a}^(2) + 2ab + {b}^(2)

Here, a is sin x

b is cos x

So


( \sin(x) + \cos(x) ) {}^(2) = \sin {}^(2) (x) + 2 \sin(x) \cos(x) + \cos {}^(2) (x)

We know


\sin {}^(2) (x) + \cos {}^(2) (x) = 1

So we know have


1 + 2 \sin(x) \cos(x)


\sin(2x) = 2 \sin(x) \cos(x)

So our final answer is


1 + \sin(2x)

User Hamdy
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